Honors Algebra 2
13.4 Sine and Cosine Graphs Worksheet
Name ________________________________________
Date________________ Hour _____________
For each function, state the amplitude, if there is a reflection, the phase shift and the vertical shift. Write “none” for
transformations that do not exist.
Then graph the function.
Step #1: Start by graphing the parent function =
if there is no period change (b).
If there is a period change, find the new intervals first, then graph the parent graph as usual.
Step #2: Write the transformations IN THE ORDER IN WHICH THEY OCCUR
Step #3: Graph each transformation – one at a time, use more than one color!!!
Step #4: Label your final graph.
1.
= sin
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
2. = 4 sin
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
3. = 2sin
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
4. = sin + 3
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
5. = sin
−4
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
6. = sin −
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
7. = − sin
+3
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
8. = −2 sin( − )
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
9. = 4 sin −
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
10. = − sin + + 1
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
11. = 3 sin( + ) − 2
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
12. = cos
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
13. =
cos
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
14. = 3 cos
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
15. = cos − 5
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
16. = cos − + 2
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
17. = 3 cos 2 − 1
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
18. = − cos
−2
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
19. = − cos( − ) − 1
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
20. = 3 cos + − 2
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
21. = −2 cos 2( − ) + 1
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
22. = cos( + 2 ) + 3
Period: __________
Amplitude:_______
Reflection:_______
Phase Shift:__________
Vertical Shift:__________
Transformations:
Directions: Match the graph with its equation by writing the appropriate letter next to the equation.
23.
y  4 sin 4 x
________
24.
y  cos  x   
________
D.
25.
y  4 cos 4 x
________
26.
y  4 sin
1
x
4
________
27.


y  sin 2  x  
2

________
28.
y  cos x  2
________
29.
1
y  cos x  1
2
E.
G.
________
F.